For example, the element
\(V=({\begin{matrix} 1 & 0 \\ -3 & 1 \end{matrix}})\) 
(equal to the monodromy around the conifold point \(\tau =0\) ) acts on
\(\tau \)  via \(V \colon \tau \mapsto -\frac{\tau }{3\tau -1}\) , and
on the derived category via the spherical twist \(ST_\mathcal {O}\)  around the spherical object
\(\mathcal {O}\) . The latter is given by the exact triangle (see (REF ) and [1]})
\(\mathrm {Hom}^\bullet _{K_{{P}^2}}(\mathcal {O},E)\otimes \mathcal {O} \xrightarrow{} E\rightarrow ST_\mathcal {O}( E ) \xrightarrow{}\) 
